Functions Contents - G
 
Integral calculus
      The definite and indefinite integrals
      The area between the graph of a function and the x-axis over a closed interval
         Geometric interpretation of the definite integral
      Properties of the definite integral
         The definite integral over interval of zero length
         Reverse order of integration
         The constant multiple rule
         The integral of the sum or difference of two functions
         Internal addition of the definite integral
         The definite integral of an odd function
         The definite integral of an even function
         The definite integral of a nonnegative and nonpositive functions
         Relationship of the definite integrals of two functions over the same interval of integration
         Absolute integrability
         The mean value theorem
         The average value of a function over the given interval
      The indefinite integral
         Integration - inverse of differentiation
         Constant of integration, the arbitrary constant term in the expression of the indefinite integral
         Evaluating the indefinite integral example
      The fundamental theorem of calculus
         The fundamental theorem of differential calculus
      Evaluating definite integrals using indefinite integrals
         The fundamental theorem of integral calculus
         Evaluating the definite integral examples
      The indefinite integral
      Basic rules of integration
         Table of indefinite integrals
      The indefinite integral applications
         Kinetic equation of free fall
         Exponential growth and decay (increase and decrease)
      Evaluation of indefinite integrals using some basic integration rules and formulas examples
         Use of basic integration rules and formulas to solve indefinite integrals
      Substitution rule
         Evaluating the indefinite integrals using substitution rule examples
         Evaluating the indefinite integrals using substitution rule solutions
         Use of the substitution rule to solve indefinite integrals examples
         Indefinite integrals of irrational functions
      Integration by parts rule
         Evaluating the indefinite integrals using the integration by parts formula examples
         Evaluating the indefinite integrals using the integration by parts formula solutions
      The indefinite integrals containing quadratic polynomial (trinomial)
         The indefinite integrals containing quadratic polynomial examples
      Recursion formulas - use of integration by parts formula
         Recursion formulas - use of integration by parts formula examples
      Substitution and definite integration
         Substitution and definite integration examples
      Integrations by parts and the definite integral
      The improper integrals
         The improper integral definition
         The improper integrals examples
      Differentiation and the integration of infinite series
         Differentiation and integration of infinite series examples
      Applications of the definite integral
      The area of a region in the plane
         The area between the graph of a curve and the coordinate axis
         The area between the graph of a curve and the coordinate axis examples
         The area bounded by a parametric curve
         The area of the sector of a curve in polar coordinates
         The area of the sector of a curve given in Cartesian (or rectangular) coordinates
         The area of the sector of a parametric curve
      The area between two curves
         The area between two curves examples
      Length of plane curve, arc length
         Arc length of a parametric curve
         Arc length of a curve in polar coordinates
      The volume of a solid of revolution
         The volume of a sphere
         The volume of a spherical segment
         The volume of a cone
      The surface area of a solid of revolution
         The lateral surface area of a cone
         The surface area of a spherical cap
         The surface area of an ellipsoid
   
 
 
 
   
 
   
   
 
 
Copyright 2004 - 2020, Nabla Ltd.  All rights reserved.